Satellites don't synchronize themselves with the Earth's rotation; they must be very carefully placed at a certain height above the Earth's equator by people in order to be geosynchronous. This height is 36,000 km above the Earth's surface. At this height, a satellite will orbit at the same angular rate as the Earth rotates, which we call a geosynchronous orbit. (If this orbit follows a path directly over the equator, it will "hover" over a single point on Earth, which is called a geostationary orbit--a special type of geosynchronous orbit.)
You may be familiar with Galileo's discovery that the speed at which an object falls (in a vacuum) is independent of the mass of the object. This is because of the fact that, while massive objects are more strongly gravitationally attracted to the Earth, they're also harder to move. These two effects balance out exactly, as explained here.
The situation for an orbiting satellite is equivalent. Heavier satellites are harder for the Earth to pull on, but the Earth pulls with a proportionally greater force such that the heavy satellites have identical orbits to light satellites. The only parameter that determines how fast the satellite circles Earth (assuming the orbit is circular) is the distance it is from Earth. It turns out that a distance of 36,000 km (from the Earth's surface) is required for the satellite to circle us once per day.
This page was last updated June 27, 2015.